Apparatus for adjusting the resonance frequency of a microelectromechanical (MEMS) resonator using tensile/compressive strain and applications therefor

ABSTRACT

A method for varying the resonance frequency of a resonator beam is disclosed. The method comprises first manufacturing a resonator beam having a first end and a second end. The resonator beam is suspended above a substrate by the first end and the second end. At least one end of the resonator beam is connected to an actuator that applies an actuation force to the resonator beam to apply tensile strain or compressive strain onto said resonator beam. By varying the amount of actuation force, the resonance frequency of the resonator beam may be tuned. Additionally, by varying the magnitude and direction of the actuation force, the resonator beam may be used as a temperature sensor or a temperature compensated resonator.

TECHNICAL FIELD OF THE INVENTION

This invention relates to microelectromechanical system (MEMS)resonators, and more particularly, to a device for adjusting theresonance frequency of a MEMS resonator using tensile/compressivestrain.

BACKGROUND OF THE INVENTION

The advantages of using single crystal semiconductors such as silicon asa mechanical material have long been recognized. For example, it'sstrength and high intrinsic quality factor make it attractive for MEMSresonant devices. It is regularly available as an integrated circuitsubstrate and can be processed using methods developed by the ICindustry. Recently, the preferred material for forming MEMS resonatorsis polycrystalline silicon, or simply, polysilicon. This material isadvantageous because it is readily used in integrated circuits (oftenused as transistor gates), provides flexibility in geometry, and ease ofuse.

MEMS resonators are now being developed for signal filtering and for useas clocks in oscillators. However, for a MEMS resonator, the resonancefrequency of the resonator after the manufacturing process is usuallydifferent from the desired value due to processing variations. Thus,although one may desire to have a MEMS resonator have a resonancefrequency of 1 GHz, during the actual manufacturing process, it isdifficult to manufacture a MEMS resonator with exactly a resonancefrequency of 1 GHz.

One of the primary parameters that affect the resonance frequency is thedimension of the resonator. While there are post-manufacturingtechniques, such as laser trimming, that may be used to adjust thedimensions, and thus the resonance frequency, of the MEMS resonator,this laser trimming is also difficult to accurately control. Therefore,it is costly and/or difficult to precisely manufacture a MEMS resonatorhaving the desired resonance frequency. Another method of adjusting thedimension of a resonator is to use local heating, which will causeexpansion of resonator. However, this technique requires a dedicatedcircuit on the IC to effectuate the local heating.

It has been found that the resonance frequency of a MEMS resonator maybe adjusted by applying tensile strain or compressive strain to theresonator. Specifically, the resonance frequency of a resonator willincrease when subjected to tensile strain and will decrease when undercompressive strain.

BRIEF DESCRIPTION OF THE FIGURES

The invention is best understood by reference to the figures whereinreferences with like reference numbers generally indicate identical,functionally similar, and/or structurally similar elements. The drawingin which an element first appears is indicated by the leftmost digit(s)in the reference number in which:

FIG. 1 illustrates a prior art bending beam MEMS resonator.

FIG. 2 is a top view of a lever arm structure for providing tensilestrain on a resonator according to the present invention.

FIG. 3 is a lever arm structure for providing compressive strain on aresonator according to the present invention.

FIG. 4 is a single arm lever structure adapted for placing tensilestrain on a resonator according to the present invention.

FIG. 5 is a single arm lever structure adapted for placing compressivestrain on a resonator according to the present invention.

FIG. 6 illustrates a dual lever arm with curved beams adapted to placetensile strain on a resonator according to the present invention.

FIG. 7 shows the apparatus of FIG. 6 during placement of tensile strainon the resonator.

FIG. 8 illustrates a curved beam dual lever arm structure using a combactuation means to induce tensile strain on a resonator according to thepresent invention.

FIG. 9 illustrates a curved beam dual lever arm structure using a combactuation means for placing compressive strain on a resonator accordingto the present invention.

FIG. 10 illustrates a heater beam for actuating a dual lever armstructure for inducing strain on a resonator according to the presentinvention.

FIG. 11 illustrates a ratcheting shaft actuation mechanism for actuatinga single lever arm structure according to the present invention.

FIG. 12 illustrates a ratcheting wedge for actuating a dual lever armstructure according to the present invention.

FIG. 13 illustrates a ratcheting wheel actuation mechanism for actuatinga resonator according to the present invention.

FIG. 14 illustrates a temperature sensor formed according to the presentinvention.

FIG. 15 illustrates a temperature corrected resonator according to thepresent invention.

FIG. 16 illustrates an alternative embodiment of a temperature correctedresonator according to the present invention.

FIG. 17 illustrates a temperature sensor formed according to analternative embodiment of the present invention.

FIG. 18 illustrates an alternative embodiment of a temperature correctedresonator according to the present invention.

FIG. 19 illustrates yet another alternative embodiment of a temperaturecorrected resonator according to the present invention.

FIG. 20 illustrates yet another embodiment of a temperature sensorformed according to the present invention.

FIG. 21 illustrates another alternative embodiment of a temperaturesensor formed according to the present invention.

FIG. 22 illustrates yet another alternative embodiment of a temperaturesensor formed according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of a means for applying tensile or compressive strain to aresonator is described in detail herein. Further these structures areapplied in the context of temperature compensated resonators andtemperature sensors. In the following description, numerous specificdetails are provided in order to provide a thorough understanding ofembodiments of the invention. One skilled in the relevant art willrecognize, however, that the invention can be practiced without one ormore of the specific details, or with other methods, materials,components, etc. In other instances, well known structures, materials,or operations are not shown or described in detail to avoid obscuringaspects of various embodiments of the invention. Furthermore, it isunderstood that the various embodiments shown in the Figures areillustrative representations, and are not necessarily drawn to scale.

Reference throughout the specification to “one embodiment” or “anembodiment” means that a particular feature, structure, material, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the present invention. Thus, theappearances of the phrase “in one embodiment” or “in an embodiment” invarious places throughout the specification are not necessarily allreferring to the same embodiment. Furthermore, the particular features,structures, materials, or characteristics may be combined in anysuitable manner in one or more embodiments.

The manufacture and use of MEMS resonators for filtering or oscillatorapplications is now being developed, with commercial adoption envisionedshortly. Typically, polysilicon is used as the resonator material. Onecommon type of MEMS resonator is the “bending beam” structure (alsoreferred to herein as a “resonator beam”). In a bending beam structure,a beam of polysilicon material is suspended above a semiconductorsubstrate by anchors at both ends of the beam. The beam is excited by anelectrical input that can induce mechanical vibration in the beam.Typically, the electrical input is provided from below the beam.

FIG. 1 shows an exemplary prior art bending beam structure. As seen inFIG. 1, a bending beam 101 is suspended at its ends above asemiconductor substrate 107 by anchors 103 and 105. The anchors 103 and105 are secured to the substrate 107. A drive electrode 109 is placedunderneath the bending beam 101. The drive electrode 109 is used toexcite the bending beam 101 into vibrating. As is known in the art, theresonance frequency of the bending beam 101 is based upon severalparameters, including the thickness of the beam, the density of thematerial forming the beam, the Young's modulus of the beam, and thelength of the beam.

Specifically,$\omega \propto {\frac{t}{L^{2}}\sqrt{\frac{E}{\rho}}\left( {1 + {\frac{L^{2}}{7t^{2}}S}} \right)}$

where t is the beam thickness, L is the beam length (the length L ismeasured between the anchors 103 and 105 of FIG. 1), E and ρ are theYoung's modulus and the density of the material of the beam, and S isthe elastic strain applied on the beam. When the temperature rises, Land t increase, but the effect of L dominates. Therefore, frequencytends to decrease.

If a compressive strain is applied with increasing temperature, then thefrequency sensitivity to temperature is enhanced. Conversely, if atemperature dependent tensile strain is applied, this may be used tocompensate for the beam expansion effect. Such a condition is governedby $\frac{\omega}{T} = 0$ or${\alpha_{b}\left( {1 + {\frac{L^{2}}{7t^{2}}S}} \right)} = {\frac{L^{2}}{7t^{2}}\frac{S}{T}}$

where α_(b) is the coefficient of thermal expansion of the beam. Forpractical situations S<<1, therefore, the applied strain must satisfy$\frac{S}{T} = {\frac{7t^{2}}{L^{2}}\alpha_{b}}$

While it is preferred that the resonance frequency of a MEMS resonatorbe precisely controlled by varying the size and characteristics of thebreathing bar or bending beam structure, in practical manufacturingprocesses, it is not always possible to precisely control theseparameters. Therefore, post-manufacturing processing, such as lasertrimming is necessary to correct the actual manufactured resonancefrequency to the desired resonance frequency. Specific details for themanufacturing and operation of a MEMS resonator can be found in“Micromachining Technologies for Miniaturized communication devices,” byC. T. C. Nguyen, Proceedings of SPIE: Micromachining andMicrofabrication, Santa Clara, Calif., Sep. 20-22, 1998, pages 24-38.

FIG. 2 illustrates a resonator beam 202 that is held on either side bylever arms 204 a and 204 b. Both the lever arm 204 a and the lever arm204 b are suspended on anchors 206, 208, and 210. The upper portion oflever arm 204 a is connected to anchor 206 by means of the flexiblesuspension tether 212 a. Similarly, the upper portion of lever arm 204 bis connected to anchor 208 through flexible suspension tether 212 b. Thelower portions of the lever arm 204 a and 204 b are connected to theanchor 210 by means of a bending pivot 214.

As seen in FIG. 2, the lever arms 204 a and 204 b are symmetric oneither side of the resonator beam 212. Because of the bending pivots 214and the suspension tethers 212 a and 212 b, thermal expansion of thesubstrate 216 upon which these elements are formed is decoupled from thesuspended structures. An open area 218 between the lever arms 204 a and204 b is provided to accommodate various possible mechanisms (describedfurther below) to provide an actuation force that moves the upperportion of lever arm 204 a towards anchor 206 and the upper portion oflever arm 204 b towards anchor 208. The lever arms 204 a and 204 b aresufficiently stiff so that its bending is negligible.

When an actuation force is provided to the lever arms 204 a and 204 b,this causes the lever arms to pivot about anchor 210 by means of bendingpivot 214. L₁ is the distance between the point of pressure by theactuation force and the bending pivot 214. L₂ is the distance betweenthe resonator beam 202 and the bending pivot 214. The ratio L₁ to L₂governs the amount of strain that is imparted onto resonator beam 202for a given actuation force. The material of the resonator beam 202 isselected to preferably have a high tensile yield stress.

Turning to FIG. 3, the position of the anchor 210 and bending pivot 214is switched with the position of the resonator beam 202. An actuationforce applied to the lever arms 204 and 204 b will cause the lever armsto pivot about anchor point 210 and result in a compressive strain to beplaced onto the resonator beam 202. Thus, whereas the structure shown inFIG. 2 causes tensile strain to be placed on to the resonator beam 202,the apparatus of FIG. 3 causes compressive strain to be placed on to theresonator beam 202. Compressive strain tends to decrease the resonantfrequency of the resonator beam 202. Tensile strain will tend toincrease the resonance frequency of the resonator beam 202.

Turning to FIG. 4, a single lever structure is shown. In this structure,a lever arm 408 is connected at anchor 404 and 412. The upper portion ofthe lever arm 408 is connected to anchor 404 by means of a suspensiontether 406. A lower portion of the lever arm 408 is connected to theanchor 412 through bending pivot 410. The resonator beam 402 has one endconnected to the lower portion of the lever arm 408 and another endconnected to the anchor 412. An actuation force applied to the upperportion of the lever arm 408, bracing against anchor 414 as a fixedsupport, causes the lever arm 408 to pivot about the bending pivot 410.This causes tensile strain to be applied to resonator beam 402.

The single lever structure of FIG. 4 is employed advantageously for usewith certain types of actuation mechanisms. Further, lever arm 408 issufficiently stiff so it's bending is negligible under actuation forces.Like above, the ratio of L₁ divided by L₂ governs the amount of strainimparted to the resonator beam 402. A large enough ratio ensures asufficiently fine strain adjustment on the resonator beam 402.

Turning to FIG. 5, the single lever structure of FIG. 4 is shown, exceptthat the positions of the resonator beam 402 and the bending pivot 410are switched. By switching these positions, an actuation force providedon to the upper portion of the lever arm 408 will cause compressivestrain to be placed on the resonator beam 402.

It should be appreciated that the lever structures shown in FIGS. 2-5are exemplary only and that many variations in their configuration arepossible. As noted above, the lever structures shown in FIGS. 2-5require an actuator to provide an actuation force on to the lever arms.As further detailed below, several different types of actuators arecontemplated in the present invention.

Specifically, turning to FIG. 6, multiple curved beams 602 may be placedbetween the upper portion of the lever arms of the structure of FIGS. 2and 3. The beams 602 are defined in the photolithography and etchingstep to be curved in the stress free state and may be formed frompolysilicon or like materials. In order to effectuate actuation forceson the lever arms, the beams (one or more) 602 are buckled into acompressive state, as shown in FIG. 7. The buckled beam 604 exerts alateral stress pushing apart the lever arms.

Depending upon how much strain is needed on the resonator beam, a curvedbeam at a particular location or several beams at various locations canbe selected to be deformed into the buckled state. A beam in a buckledstate 604 applies strain to the resonator beam. Theoretical or empiricalmodels may be used to select the appropriate beams for bucklingdeformation.

Turning to FIG. 8, a comb structure for causing the buckling of thecurved beam 802 may be employed, the comb structure 804 when activatedwill pull on the beam 802. Preferably, the beam 802 is curved in adirection opposite to the direction upon which the comb structure 804pulls. When the comb structure 804 is pulling, the beam 802 reduces itscurvature and therefore undergoes compression, transmitting force to thelever arms. This configuration is capable of much larger forces exertingon the lever arms compared to direct pulling on the lever arms usingcomb structures.

FIG. 9 shows a similar mechanism where a comb structure 904 is pullingon a curved beam 902. In this embodiment, the curved beam 902 in itsstress free state is curved towards the comb structure 904. When thecomb structure 904 is pulling, the curved beam 902 increases itscurvature and therefore undergoes a tensile stress that exerts a pullingforce in the lever arms. This configuration is capable of much largerforces exerted on the lever arms compared to direct pulling on the armsusing comb structures.

FIG. 10 illustrates another type of actuation mechanism that can exertactuation forces on to the lever arms. In particular, FIG. 10 shows alarge coefficient of thermal expansion (CTE) beam 1002 that is placedbetween the lever arms. The CTE beam 1002 includes a heater 1004integrated herein. The heater 1004 may be, for example, a resistiveheater. By controlling the temperature of the CTE beam 1002, varyingamounts of strain can be applied to the resonator beam. In oneembodiment, the CTE beam 1002 may consist of a single material thatcould be used for linear expansion. Alternatively, the CTE beam 1002 maybe a bimorph composite that bends when undergoing a temperature change.Different material combinations can produce effective expansion orcontraction when heated by the heater 1004.

FIG. 11 illustrates yet another actuation mechanism referred to as aratcheting shaft. As seen in FIG. 11, a ratcheting shaft 1102 isconnected to an anchor 1104 through a bending support 1106. Theratcheting shaft 1102 is moved to pivot about bending support 1106 by acomb structure 1108. By activating the comb structure 1108, theratcheting shaft will engage various positions of ratcheting teeth 1110.The ratcheting shaft 1102 when engaged with ratcheting teeth 1110 causeactuation forces to push on the lever arm. Thus, by pushing/pulling onthe ratcheting shaft 1102 so that its tip is locked at various positionson the ratcheting teeth 1110, various amounts of strain can be achievedon the resonator beam.

FIG. 12 shows another type of ratcheting mechanism referred to as aratcheting wedge. As seen in FIG. 12, a wedge 1202 is placed betweenlever arms 1204 and 1206. The wedge has teeth that engage withprotrusions on the lever arm 1204 and 1206. By placing the wedge so thatit is locked at various positions, various amounts of strain can beachieved on the resonator 1208.

Optionally, the wedge 1202 may be constructed out of a magnetic materialthat will exert force to drive the wedge into position in response tothe application of a magnetic field. By engaging the ratchets, the forceon the resonating number 1208 is maintained even after the magneticfield is removed.

Alternatively, a method for releasing the ratchet to permit retuning ofthe device may also be incorporated. This may take the form of a releasecatch 1210 or hook suitable for external manipulation with a microprobe.Alternatively, the release catch may take the form of a magnetic alloythat responds to application of a magnetic field. In the event that bothmagnetic actuation of the wedge 1202 and a release mechanism isemployed, it is advantageous for the orientation of the magnetic fieldthat drives the wedge actuation to be substantially perpendicular to theorientation of the magnetic field used to drive the ratchet releasemechanism.

Turning to FIG. 13, a ratcheting wheel actuation mechanism is shown. Inthis embodiment, a ratcheting wheel 1302 with ratcheting teeth can beused to set strain. In particular, the ratcheting wheel 1302 engages ananchor 1304 with the ratcheting teeth. The amount of strain on theresonator beam 1306 depends upon the rotation of the ratcheting wheel1302. The ratcheting wheel 1302 can be actuated by electrostatic force,a comb drive, or externally.

With the description of lever arm structures and associated actuationsstructures for providing tensile strain or compressive strain on to aresonator beam described above, an application of such technology is nowdescribed. In particular, it has been found that the resonance frequencyof a microbridge beam is related to its dimension and other physicalperimeters. As previously noted, as the temperature rises, both thelength of the microbridge beam and the thickness of the beam increases.However, the effect of the change in length dominates, so that frequencytends to decrease as temperature increases.

If a compressive strain is applied which is monotonically increasingwith temperature, then the frequency sensitivity to temperature isexacerbated. Conversely, if a temperature dependent tensile strain isapplied, this may be used to compensate for the beam expansion affect.Thus, the application of a tensile strain can be used to compensate fortemperature variation, and therefore, a resonator may be made to berelatively temperature stable. In a different application, by having acompressive strain be applied to the resonator beam increasing withtemperature, then the frequency sensitivity of the resonator beam totemperature can be enhanced. In such a situation, the resonator beam canbe used as a temperature sensor.

Specifically, as seen in FIG. 14, an expansion bar 1402 made of amaterial with a relatively large thermal expansion coefficient (α_(e))is placed between two lever arms 1404 and 1406. As the temperatureincreases, the expansion bar 1402 expands disproportionally and appliesan actuation force onto the lever arms 1404 and 1406. Because of thepositioning of the bending pivot 1408 and the resonator beam 1410, thisin turn causes a compressive strain to be placed onto the resonator beam1410. This will reduce the resonance frequency of the resonator bar1410. The compressive strain applied on the resonator beam 1410 isapproximately governed by:

S=(α_(e)−α_(b))ΔTL ₂ /L ₁

where α_(b) is the coefficient of thermal expansion for the resonatorbeam 1410.

Thus, the arrangement set forth in FIG. 14 tends to enhance the effectof a temperature change on the resonance frequency of the resonator bar1410. In particular, as the temperature increases, this will generallycause the resonator beam 1410 to have a lower resonance frequency.Additionally, because the expansion bar 1402 causes a compressive strainon the resonator beam 1410, this also causes a decrease in the resonancefrequency. In such a situation, a temperature sensor that has enhancedfrequency response to temperature is provided. By measuring theresonance frequency of the resonator beam 1410, temperature can beextrapolated using calibration and empirical methods.

Turning to FIG. 15, a temperature corrected resonator is shown. In thisembodiment, the position of the bending pivot 1408 and the resonator bar1410 have been reversed from FIG. 14. The result is that a rise intemperature causes the expansion bar 1402 to exert a tensile strain onthe resonator beam 1410. The tensile strain on resonator beam 1410 tendsto increase the resonance frequency. This then tends to counterbalancethe beam expansion effect due to the rise in temperature. The tensilestrain applied to the beam is approximately:

S=(α_(e)−α_(b))ΔTL ₂ /L ₁

where α_(b) is the coefficient of thermal expansion for the resonatorbeam 1410.

To make the resonator beam 1410 completely insensitive to temperature,it is required that:

dS/dT=7t ² /L ²α_(b)

Combining the two equations above we have the ratio:

L ₂ /L ₁=7t ² /L ²α_(b)/(α_(e)−α_(b))

However, in this particular lever structure, because the ratio L₂divided by L₁ is less than one, it may not be possible to completelymake the resonator beam 1410 to be totally insensitive to temperature.

Turning to FIG. 16, in an alternative embodiment, the expansion bar 1402and the resonator beam 1410 are switched positionally. In such anarrangement, if the structure FIG. 15 cannot satisfy the requirement forcomplete temperature insensitivity, by modifying the lengths of thelever arms L₂ and L₁, it may be possible to use the arrangement of FIG.16 to completely satisfy temperature insensitivity.

Turning to FIG. 17, a temperature sensor is shown. In this structure,large expansion bars 1702 and 1704 are made of a material having arelatively large thermal expansion coefficient. The entire structure issuspended on anchors 1706, 1708, 1710, and 1712. The structure issuspended to the anchors by means of suspension tethers. This designdecouples the thermal expansion of the substrate from the suspendedstructures. As the temperature rises, the expansion bars 1702 and 1704expand, applying a compressive strain on the resonator beam 1714,therefore further reducing the frequency of the resonator beam 1714. Asnoted above, the increase in temperature will tend generally to lowerthe resonance frequency of the resonator beam 1714. The ratio D₁/D₂governs the sensitivity. The compressive strain applied on the resonatorbeam 1714 is approximately:

S=2(α_(e)−α_(b))ΔTD ₁ /D ₂

FIG. 18 shows a structure similar to that of FIG. 17 except that theposition of the expansion bars 1702 and 1704 have been changed. As thetemperature rises, the expansion bars 1702 and 1704 expanddisproportionately, applying a tensile strain on the resonator beam1714, therefore counterbalancing the beam expansion effect. This resultsin a temperature corrected resonator. The tensile strain applied on theresonator beam 1714 is:

S=(α_(e)−α_(b))ΔTD ₁ /D ₂

To make the beam completely insensitive to temperature, it is requiredthat:

dS/dT=7t ² /L ²α_(b)

Combining the two equations above, we have the ratio:

D ₁ /D ₂=7t ² /L ²α_(b)/(α_(e)−α_(b))

FIG. 19 illustrates a simple way of applying temperature sensitivecompressive or tensile strain using the mismatch between the substrateand resonator beam coefficient of thermal expansions. In particular, aresonator beam 1902 is suspended between two anchors 1904 and 1906. Theanchors 1904 and 1906 are formed on a substrate 1908. The resonator beam1902 is made of a first material and the substrate is made of a secondmaterial. If there is a large mismatch between the thermal expansioncoefficience of the resonator beam 1902 and the resonator substrate1908, this mismatch can be used. For example, if the thermal expansioncoefficient of the substrate is smaller than the thermal expansioncoefficient of the resonator structure, then, as the temperature rises,the substrate 1908 may expand less, applying a compressive strain on theresonator beam 1902. This will reduce the frequency of the resonatingbeam 1902, thereby acting as a temperature sensor. The ratio H₁/H₂governs the sensitivity. The compressive strain applied on the beam isapproximately:

S=(α_(b)−α_(s))ΔTH ₁ /H ₂

Where α_(s) is the coefficient of thermal expansion of the substrate.

If the thermal expansion coefficient of the substrate is larger than thethermal expansion coefficient of the resonator beam 1902, then thestructure can be used as a temperature compensated resonator. Therequired condition is:

H ₁ /H ₂=7t ² /L ²α_(b)/(α_(s)−α_(b))

However, the above relationship may not be satisfied in some cases wherethere is the constraint of H₁/H₂ be greater than one for this geometry.

Turning to FIG. 20, a symmetric double lever structure utilizing thermalmismatch between the substrate and the resonator beam material is usedadvantageously. If the thermal expansion coefficient of the substrate2002 is greater than the thermal expansion coefficient of the resonatorbeam 2004, this will tend to apply compressive strain on the resonatorbeam 2004, therefore further reducing the resonance frequency of theresonator beam 2004. This can be used again as a temperature sensor.

If, however, the thermal expansion coefficient of the resonator beam2004 is greater than that of the substrate 2002, then a tensile straindevelops in the resonator beam 2004 as the temperature rises. Thiscounterbalances the beam expansion effect and the resonator beam istemperature compensated.

Turning to FIG. 21, this structure is similar to that of FIG. 20 exceptthat the positions of the bending pivot and the resonant beam 2004 areswitched. In this situation, if the thermal expansion coefficient of thesubstrate is less than that of the resonator beam 2004, this will resultin the application of a compressive strain on the resonator beam 2004with a rise in temperature. This will further reduce the resonancefrequency and would be suitable for an enhanced temperature sensor.

If, however, the thermal expansion coefficient of the substrate 2002 isgreater than that of the resonator beam 2004, tensile strain develops inthe resonator beam 2004 as the temperature rises, counterbalancing thebeam expansion effect. This will find application for use in atemperature compensated resonator.

Finally, turning to FIG. 22, a double cantilever structure with aresonator beam 2202 placed between two lever arms 2204 and 2206 isshown. If the thermal expansion coefficient substrate is greater thanthat of the resonator beam 2202, a substrate 2208 expandsdisproportionately with temperature, applying a compressive strain on aresonator beam 2202. This further reduces the resonance frequency andsuch an arrangement may be used as a temperature sensor. For the samestructure, if the thermal expansion coefficient of the substrate 2208 isless than that of the resonator beam 2202, a tensile strain develops inthe resonator beam 2202 if the temperature rises, therebycounterbalancing the beam expansion effect.

The above description of illustrated embodiments of the invention,including what is described in the abstract, is not intended to beexhaustive or to limit the invention to the precise forms disclosed.While specific embodiments of, and examples for, the invention aredescribed herein for illustrative purposes, various equivalentmodifications are possible within the scope of the invention, as thoseskilled in the relevant art will recognize. For example, while thebending beam and breathing bar types of mechanical resonators have beendescribed, other types of mechanical resonators may also be substitutedinto the concepts and ideas of the present invention.

These modifications can be made to the invention in light of the abovedetailed description. The terms used in the following claims should notbe construed to limit the invention to the specific embodimentsdisclosed in the specification and the claims. Rather, the scope of theinvention is to be determined entirely by the following claims, whichare to be construed in accordance with established doctorines of claiminterpretation.

What is claimed is:
 1. A method comprising: providing a resonator beamhaving a first end and a second end, the resonator beam suspended abovea substrate by the first end and the second end; providing a lever arm,the lever arm being connected to a pivot and to the first end of theresonator beam; and using an actuator to apply an actuation force to thelever arm to apply strain onto the resonator beam, wherein the positionson the lever arm where the first end of the resonator beam is connectedand where the actuation force is applied are on the same side of thepivot.
 2. The method of claim 1 wherein the actuator is a combstructure.
 3. The method of claim 1 wherein the actuator is a ratchetwheel.
 4. The method of claim 1 wherein the actuator is a ratchet wedge.5. The method of claim 1 wherein the actuator is a large coefficient ofthermal expansion heater.
 6. The method of claim 1 wherein the actuatoris a ratcheting shaft.
 7. The method of claim 1 wherein the actuator isan expansion bar that provides the actuation force proportional to atemperature.
 8. The method of claim 1 wherein the actuation forcesupplied by the actuator is proportional to a temperature.
 9. The methodof claim 8 wherein a tensile strain is applied to the resonator beam asthe temperature increases.
 10. The method of claim 8 wherein acompressive strain is applied to the resonator beam as the temperatureincreases.
 11. The method of claim 2 wherein the comb structure exertsforce on a curved beam that in turn transmits force onto the lever arm.12. The method of claim 1 further comprising connecting the second endof the resonator beam to a second lever arm and using the second leverarm in concert with the first lever arm to apply a strain to theresonator beam.
 13. The method of claim 12 the actuator applies theactuation force to both the lever arm and the second lever arm.
 14. Themethod of claim 12 wherein the lever arm and the second lever arm rotateabout the pivot to proportionally modify the amount of strain applied tothe resonator beam.
 15. A method comprising: providing a resonator beamhaving a first end and a second end, the resonator beam suspended abovea substrate by the first end and the second end; applying an actuationforce to at least one of the first end and the second end, the actuationforce creating a temperature-dependent compressive strain in theresonator beam.
 16. The method of claim 15 wherein the actuation forceis proportional to a temperature.
 17. The method of claim 15 whereinapplying the actuation force comprises using an actuator, wherein theactuator is a large coefficient of thermal expansion heater.
 18. Themethod of claim 15 wherein applying the actuation force comprises usingan actuator, wherein the actuator is an expansion bar that provides theactuation force proportional to a temperature.
 19. The method of claim15 wherein a compressive strain is applied to the resonator beam as thetemperature increases.
 20. A method comprising: providing a resonatorbeam having a first end and a second end, the resonator beam suspendedabove a substrate by the first end and the second end; providing a leverarm, the lover arm being connected to a pivot and to the first end ofthe resonator beam; and using an actuator to apply an actuation force tothe lever arm to apply strain onto the resonator beam, wherein thepositions on the lever arm where the first end of the resonator beam isconnected and where the actuation force is applied are on opposite sidesof the pivot.
 21. The method of claim 20 wherein the actuator is a combstructure.
 22. The method of claim 20 wherein the actuator is a ratchetwheel.
 23. The method of claim 20 wherein the actuator is a ratchetwedge.
 24. The method of claim 20 wherein the actuator is a largecoefficient of thermal expansion heater.
 25. The method of claim 20wherein the actuator is a ratcheting shaft.
 26. The method of claim 20wherein the actuator is an expansion bar that provides the actuationforce proportional to a temperature.
 27. The method of claim 20 whereinthe actuation force supplied by the actuator is proportional to atemperature.
 28. The method of claim 20 wherein a tensile strain isapplied to the resonator beam as the temperature increases.
 29. Themethod of claim 20 wherein a compressive strain is applied to theresonator beam as the temperature increases.
 30. The method of claim 21wherein the comb structure exerts force on a curved beam that in turntransmits force onto the lever arm.
 31. The method of claim 20 furthhercomprising connecting the second end of the resonator beam to a secondlever arm and using the second lever arm in concert with the first leverarm to apply a strain to the resonator beam.
 32. The method of claim 31wherein the actuator applies the actuation force to both the lever armand the second lever arm.
 33. The method of claim 31 wherein the leverarm and the second lever arm rotate about the pivot to proportionallymodify the amount of strain applied to the resonator beam.